# Using the following equation, find the center and radius: x^{2 }- 2x + y^{2 }- 6y = 26

**Solution:**

The general equation of a circle is given by:

(x - h)^{2} + (y - k)^{2}= r^{2} --- (1)

The circle represented by the above equation is of radius r and centered at coordinates (h, k)

The given equation x^{2 }- 2x + y^{2 }- 6y = 26 can be converted into the equation form given in (1) above.

x^{2}- 2x + y^{2 }- 6y = 26

Adding 1 and 9 on both sides of the equality we get:

(x^{2 }- 2x + 1) + (y^{2 }- 6y + 9) = 26 + 1 + 9

(x - 1)^{2} + (y - 3)^{2} = 36

(x - 1)^{2} + (y - 3)^{2} = 6^{2 }--- (2)

Equation (2) now represents a circle with

Radius r = 6 and centered at coordinates (1, 3)

## Using the following equation, find the center and radius: x^{2 }- 2x + y^{2 }- 6y = 26

**Summary:**

The equation x^{2 }- 2x + y^{2 }- 6y = 26 represents a circle centered at (1, 3) and has a radius ‘r’ = 6.